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Adaptive R charts with variable parameters

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  • Lee, Pei-Hsi

Abstract

The Shewhart R control chart (R chart) has been widely used to monitor process variance. However, the main disadvantage of an R chart is its slowness to signal small increases on the variability. In this paper, ideas of adaptive control charts are extended to the Shewhart R chart for improving efficiency in signaling increases on the variance. A Markov chain model is applied to evaluate its performance. The statistical performance shows that the R chart with variable parameters (VP) is more sensitive to variance increases.

Suggested Citation

  • Lee, Pei-Hsi, 2011. "Adaptive R charts with variable parameters," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 2003-2010, May.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:5:p:2003-2010
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    References listed on IDEAS

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    1. Lin, Yu-Chang & Chou, Chao-Yu, 2007. "Non-normality and the variable parameters control charts," European Journal of Operational Research, Elsevier, vol. 176(1), pages 361-373, January.
    2. He, David & Grigoryan, Arsen, 2006. "Joint statistical design of double sampling and s charts," European Journal of Operational Research, Elsevier, vol. 168(1), pages 122-142, January.
    3. Luo, Yunzhao & Li, Zhonghua & Wang, Zhaojun, 2009. "Adaptive CUSUM control chart with variable sampling intervals," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2693-2701, May.
    4. De Magalhaes, Maysa S. & Epprecht, Eugenio K. & Costa, Antonio F. B., 2001. "Economic design of a Vp chart," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 191-200, December.
    5. Shu, Lianjie & Jiang, Wei & Wu, Zhang, 2008. "Adaptive CUSUM procedures with Markovian mean estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4395-4409, May.
    6. Torng, Chau-Chen & Lee, Pei-Hsi & Liao, Nai-Yi, 2009. "An economic-statistical design of double sampling control chart," International Journal of Production Economics, Elsevier, vol. 120(2), pages 495-500, August.
    7. Giovanni Celano, 2009. "Robust design of adaptive control charts for manual manufacturing/inspection workstations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 181-203.
    8. Chen, Yan-Kwang & Hsieh, Kun-Lin, 2007. "Hotelling's T2 charts with variable sample size and control limit," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1251-1262, November.
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    Cited by:

    1. Hedegaard, Esben & Hodrick, Robert J., 2016. "Estimating the risk-return trade-off with overlapping data inference," Journal of Banking & Finance, Elsevier, vol. 67(C), pages 135-145.
    2. Lee, Pei-Hsi, 2013. "Joint statistical design of X¯ and s charts with combined double sampling and variable sampling interval," European Journal of Operational Research, Elsevier, vol. 225(2), pages 285-297.
    3. Guoyi Zhang, 2014. "Improved R and s control charts for monitoring the process variance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1260-1273, June.

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